Example 1 Add the following harmonic motions analytically and check the solution graphically.

x1 = 4 cos (wt + 100)

x2 = 6 sin (wt + 600)

Solution

Graphical Method

Let us put the two equations as
x1 = 4 cos(wt + 10 0 ) = 4 sin(wt + 1000 )
and x2 = 6 sin (wt + 600 )
Now both the equations are in the same form, the vector diagram can be drawn as shown
in the adjoining figure.